There is an important terminology for logical conditions and their relationship when dealing with proof of theorems. It is important to be familiar with it to properly understand what exactly a theorem states.
Usually, theorem states something like "If [some condition is true] then [some other condition is true]". Equally acceptable formulation is "From [some condition is true] follows [some other condition is true]".
If from a statement A (e.g. some condition is true) follows statement B (e.g. some other condition is true) we say that A is sufficient condition for B. At the same time we say that B is necessary condition for A. Another term is that "A implies B". Yet another way of saying the same thing is "B can be inferred from A".
Sufficient condition for "not getting wet" if it is raining is "staying indoors". It is certainly not a necessary condition because you will not get wet if you are in a car or properly dressed and equipped with an umbrella. We can also say that condition of "not getting wet" is a necessary condition (the one that follows from) for "staying indoors".

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